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प्रश्न
For arithmetic progression, first term is – 8 and last term is 55. If sum of all these terms is 235, find the number of terms and common difference.
उत्तर
Let a and d represent the first term and common difference, respectively.
So, a = – 8, an = 55 , and Sn = 235
We know, `S_n = n/2 (a + a_n)`
⇒ 235 = `n/2(-8 + 55)`
⇒ 470 = n(47)
⇒ n = 10
Now, an = a + (n – 1)d
⇒ 55 = – 8 + (10 – 1)d
⇒ 55 + 8 = 9d
⇒ 63 = 9d
⇒ d = 7
Hence, the number of terms is 10 and common difference is 7.
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